What kind of knife and what kind of bat? And what sort of locale would this hypothetical fight be in? Are we talking about a fight in a clear, level, open space (like a gladiatorial arena), or a street fight, or a fight inside a building? There's so many factors that affect the choice. For me, personally, I'd feel more comfortable with a good sized knife over something like a cricket or rounders bat but if the bat is a full sized baseball bat I'd probably take that.

Assuming the arena is clear and level, that my opponent is as lacking in experience and training as I am, that the knife is a single straight edge and as big as a large chef's knife and that the bat is a full sized baseball bat made of metal, and also assuming that the weapons are chosen before entry into the arena... I'd probably err on the side of caution and pick the bat. The extra reach just pips the decision. Then I could walk calmly toward my opponent, gauging his approach, calculating possible actions of attack and defence.

If the weapons are the same but are placed on the ground exactly in the middle between me and my opponent and assuming that the fight can't be started until a weapon is held... I'll pick the knife and hope that I can get to the knife just before my opponent gets there. This is purely because of the speed and damage type within that small window of opportunity. We'd be too close to each other at that moment for the bat to be useful without serious forethought or training.